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系統識別號 U0002-1607200915120200
中文論文名稱 對數線性混合效用測量誤差模型之ㄧ致性估計
英文論文名稱 A Consistent Estimation in Log-Linear Mixed Measurement Error Models
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 97
學期 2
出版年 98
研究生中文姓名 張瑞君
研究生英文姓名 Jui-Chun Chang
學號 696190387
學位類別 碩士
語文別 英文
口試日期 2009-06-24
論文頁數 22頁
口試委員 指導教授-黃逸輝
委員-黃文瀚
委員-溫啓仲
中文關鍵字 改正分數  對數線性模型  測量誤差  混合效用  準變異數函數 
英文關鍵字 Corrected score  Log-linear model  Measurement errors  Mixed effects  Quasi-variance function 
學科別分類 學科別自然科學數學
中文摘要 將隨機效用引進迴歸模型裡,反應變數之間就會具有相關性。因此當模型包括隨機效用時,也就是所謂的混合模型,便可以用來模式化具有相關性反應變數的資料。在大多數的混合模型裡,以概似函數為基礎的推論通常是可行的,然而當迴歸模型裡有任何共變數受限於測量誤差時,統計推論的工作就會變得困難,因為在大部分的測量誤差問題裡概似函數是無界的也通常是不可行的,尤其是在自變數是未知參數的時候。因此至今只有少數的文獻討論處理有測量誤差的混合模型。就作者所知,在對數線性混合效用模型且自變數受限於測量誤差時,目前尚未有人提出一個具有一致性的估計方法。在本篇論文裡,我們將利用準變異數函數與校正分數的概念,在傳統加法性的測量誤差假設下,提出一種具有一致性的估計方法,而我們的模擬研究也顯示這個估計函數的表現是不錯的。
英文摘要 By introducing the random effect into a regression model, the correlation between responses raises consequently. Thus when a model includes random effects, which is called a mixed model, can be suitable for modeling correlated responses. In most mixed models, the likelihood-based inferences are usually applicable. However, when any covariate in the regression model are subject to measurement error, the statistical inference becomes difficult for the reason that the likelihood approach is not feasible in most measurement error problems, especially for the functional cases. For this difficulty, there are only few literatures dealing with the mixed model with measurement error nowadays. Furthermore, to the best knowledge of the author, there is no consistent estimation for the log-linear mixed effect model when measurement error presents. In this thesis, inspired by the quasi-variance function and the corrected score, we construct estimating function for log-linear mixed model with classical additive measurement error. It is shown that the estimation is consistent and our simulation study indicates that the proposed estimating function works satisfactory.
論文目次 Contents
1 Introduction 1
2 The Model And Regression Calibration Approach 2
3 The Weighted and Corrected Score Function 5
3.1 When There Are Replicates 7
4 Simulation 8
5 Discussion 19
Appendix 20
References 22

Table of contents
Table 1 10
Table 2 10
Table 3 11
Table 4 11
Table 5 12
Table 6 12
Table 7 13
Table 8 13
Table 9 14
Table 10 14
Table 11 15
Table 12 15
Table 13 16
Table 14 16
Table 15 17
Table 16 17
參考文獻 1 Carroll, R. J., Ruppert, D., Stefanski, L. A. & Crainiceanu, C. M. (2006). Measurement error in nonlinear models. Chapman and Hall, New York.
2 Guo, J. Q. & Li, T. (2002). Poisson regression models with errors-in-variables: implication and treatment. Journal of statistical planning and inference 104, 391-401.
3 Harville, D. A. (1977). Maximum likelihood approaches to variance component estimation and related problems. Journal of the American Statistical Association 72, 320-340.
4 Huber, P. J. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. Proc. Fifth Berkeley Symp. Math. Statist. Prob., 1, 221-233.
5 McCullagh, P. & Nelder, J. A. (1990). Generalized linear models. Chapman and Hall London.
6 McCulloch, C. E. & Searle, S. R. (2001). Generalized linear, and mixed models. Wiley, New York.
7 Nakamura, T. (1990). Corrected score function for errors-in-variables models: Methodology and application to generalized linear models. Biometrika 77, 127-37
8 Robinson, G. K. (1991).That BLUP is a good thing: The estimation of the random effects. Statist. Sci.6, 15-51.
9 Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models and Gauss-Newton method. Biometrika, 61, 439-447.
10 Wang, N., Lin, X., Gutierrez, R. & Carroll R. J. (1998). Bias analysis and SIMEX approach in generalized linear mixed measurement error models. J. Amer.Statist.Assoc.93, no. 441, 249-261.
11 Zeger, S. L. & Edelstein, S. L. (1989). Poisson regression with a surrogate X; an analysis of vitamin A and Indonesian children's mortality. Appl.Statist.38, 309-318.
12 Zhong, X. P., Fung, W. K. & Wei, B. C. (2002). Estimation in linear models with random effects and errors-in-variables*. Ann.Statist. 3, 595-606.
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